Chaotic zones around gravitating binaries

TL;DR

This paper analytically estimates the size of chaotic orbital zones around binary systems, showing how resonance overlap leads to chaos and potential ejection of tertiary bodies, depending on mass ratios and eccentricities.

Contribution

It introduces an analytical method using separatrix map theory to determine the emergence of chaotic zones in binary systems based on mass ratios and orbital resonances.

Findings

Chaotic zones form when mass ratios exceed a threshold due to resonance overlap.

The size of the chaotic zone depends on the tertiary's orbital eccentricity.

Observed exoplanetary configurations align with the predicted mass ratio threshold.

Abstract

The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries (a double star, a double black hole, a binary asteroid, etc.) is estimated analytically, in function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries mass parameter threshold.